Deep Component Analysis via Alternating Direction Neural Networks
This work addresses the problem of integrating theoretical insights from shallow models into deep learning for researchers and practitioners, though it appears incremental in bridging existing paradigms.
The paper tackles the gap between deep neural networks' performance and shallow component analysis' theory by introducing Deep Component Analysis (DeepCA), a multilayer model with hierarchical constraints, and demonstrates performance improvements on tasks like single-image depth prediction with sparse constraints.
Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich intuition and theory, but smaller capacity often limits its usefulness. To bridge this gap, we introduce Deep Component Analysis (DeepCA), an expressive multilayer model formulation that enforces hierarchical structure through constraints on latent variables in each layer. For inference, we propose a differentiable optimization algorithm implemented using recurrent Alternating Direction Neural Networks (ADNNs) that enable parameter learning using standard backpropagation. By interpreting feed-forward networks as single-iteration approximations of inference in our model, we provide both a novel theoretical perspective for understanding them and a practical technique for constraining predictions with prior knowledge. Experimentally, we demonstrate performance improvements on a variety of tasks, including single-image depth prediction with sparse output constraints.